682 Mr. C. G. Darwin on the 



Suppose that the intensity of" the monochromatic incident 

 beam at a distance R is I/R 2 , and that the whole effect is 

 observed in an instrument having a slit of length I and 

 sufficient breadth to include the whole beam. Then the 

 instrument will measure 



l C C- s'de C" s'de ■) 



p U— (e~ V.e 2 -* 2 ) 2 ' 1. (e+ sJ^-s'fV 



which reduces to 



T Z 8 



p & 



If we put in the value of s this reduces to 



I-^N|/(2<£,£)|\ 2 cosec20. . . (10) 



Of the two polarized components that for which the electric 

 vibration is in the plane of incidence has in its / a factor 

 cos</>*. Introducing this and also the temperature factor f 

 we have 



j-j 8 l+lcos2<ft l N , , ]e -^ ( ^ 2 X 2 cosec 2<l>. (11) 

 p '6tt 2 ' 



As in the earlier paper, we next find the result of limiting 

 the incident beam by a slit. To describe the diffractive 

 effect of a slit it is usual to imagine that every point of the 

 slit gives out a spherical wave, and that the separate waves 

 are coherent. For our purpose it is better to resolve the 

 waves from the slit into a set of plane waves. The amplitude 

 of any of these waves is given by a Fresnel integral taken 

 between the proper limits. The amplitude of reflexion in 

 any direction will be determined by the product of this 

 Fresnel integral and the reflexion factor for the correspond- 

 ing direction. Let the slit be at a distance r from the source 

 and of angular breadth cr. Then we saw in the earlier paper % 

 that the intensity opposite the centre of the slit has practU 



kr 

 cally its full value when o 2 — =6, and so if the slit is placed 



symmetrically with regard to the reflexion, the intensity of 

 reflexion has its full value at the central point. If we take 

 &=10 9 and r = 30 cm. this gives cr = 5". Now we know that 



* Loc cit. p. 326. 



t Loc. cit. p. 325. The expression used is not applicable to low- 

 temperatures. 

 % Loc. cit. p. 323. 



